Trump at the White House on Thursday. The president told reporters earlier this month he did not know about the $130,000 payment Cohen made to Stormy Daniels.
Photograph: Nicholas Kamm/AFP/Getty Images

Donald Trump has acknowledged for the first time that his lawyer Michael Cohen represented him in the “crazy Stormy Daniels deal” – despite having previously denied knowing about a $130,000 hush payment arranged by Cohen to silence the adult film star, who claims to have had sex with him more than a decade ago.

“He represents me, like with this crazy Stormy Daniels deal, he represented me,” Trump said in a half-hour interview with the morning TV show Fox & Friends. “From what I’ve seen, he did absolutely nothing wrong. There were no campaign funds going into this, which would have been a problem.”

Within hours, the admission prompted a fresh court filing from federal prosecutors in New York investigating Cohen’s business dealings, arguing that the president’s comment undermines Cohen’s claim that records seized by the FBI in that case should be protected by attorney-client privilege.

The admission and filing came ahead of the latest court hearing in Cohen’s criminal case in New York on Thursday afternoon. The events represented the latest twist in the drama that has been playing out since Daniels sued Trump in March in Los Angeles, alleging that Cohen paid to silence her during the election campaign, and then the FBI raided Cohen in April.

On Wednesday, Cohen said he plans to plead the fifth amendment in the civil case and asked the LA court for a delay while the parallel case plays out in New York.

Earlier this month, Trump told reporters aboard Air Force One that he did not know about the payoff or where Cohen had got the money. When asked why Cohen made the payment, Trump said: “You’ll have to ask Michael Cohen. Michael is my attorney. You’ll have to ask Michael.”

Butduring the interview with Fox & Friends on Thursday morning, Trump appeared to reveal that he was aware of Cohen’s payment to Daniels.

Cohen reportedly paid Daniels the money to keep her quiet about claims she had an affair with Trump. Daniels has sued to release herself from a non-disclosure agreement that she signed in 2016, arguing that it was void because Trump never signed it.

Trump, meanwhile, on Thursday sought to distance himself from Cohen, his lawyer and fixer for over a decade.

“Michael is in business, he is really a businessman, a fairly big business, as I understand it,” Trump said. “I don’t know his business, but [the investigation] doesn’t have to do with me.”

He added that Cohen “also practices law” but handled only a “tiny, tiny little fraction” of Trump’s “overall legal work”.

The hush-money payment to Daniels is reportedly a focus of a federal investigation into Cohen’s private finances and business interests. Investigators are likely to examine whether the payment was legal under election campaign finance laws and whether Cohen disclosed the true reason for borrowing the funds.

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Michael Avenatti, a lawyer for Stormy Daniels, called Trump’s comments a “hugely damaging admission” and said they help to burnish her case.

“He now has backtracked and now admits that Michael Cohen represented him in connection with the Stormy Daniels matter and that directly contradicts what he said,” Avenatti said on MSNBC.

Following Trump’s interview, federal prosecutors hit back afresh against claims by Cohen thatrecords seized by the FBI should be off-limits. Fox News host Sean Hannity, who was also revealed in court as one of Cohen’s clients, has made a similar argument.

“These statements by two of Cohen’s three identified clients suggest that the seized materials are unlikely to contain voluminous privileged documents, further supporting the importance of efficiency here,” Robert Khuzami, the deputy US attorney for the southern district of New York, wrote in a letter filed on Thursday.

Lawyers for Trump and Cohen have sought to restrict what prosecutors are able to review based on a claim of attorney-client privilege.

In the same, wide-ranging interview with Fox on Thursday, Trump turned once again to the investigation by special counsel Robert Mueller into whether his campaign colluded with Russia to meddle in the 2016 presidential election, and took contrary views in quick succession.

“Because of the fact that they have this witch-hunt going on … I‘ve taken the position – and I don’t have to take this position, and maybe I’ll change – that I will not be involved with the justice department,” he said, then later added: “Our justice department, which I try and stay away from but at some point I won’t” should not be focused on the “nonsense of collusion with Russia”.

Trump also wished his wife, Melania, a happy birthday and said he chose the interview datein honor of the occasion. Asked what he got her, Trump said he had better not saybecause “maybe I didn’t get her so much”, adding: “I got her a beautiful card. You know I’m very busy.”